Question

What is event of getting a number greater or equal to 3 when rolling a die?

Answer 1

The probability is `2/3`
(presuming that, by "event" you meant "probability")

Explanation:

The roll of a fair die is conventionally modelled as though there are six possible mutually exclusive outcomes, each with their own individual probability (which, by symmetry, is equal to all of the others), and each of a value such that they sum to `1` (so that all possible outcomes are exhaustively included in the probability outcome "state space" of the model).

Denoting one such outcome by P(X), noting that there are six such outcomes, all of which are equal, it is possible to write

`6 P(X) = 1`

so that

`P(X) = 1/6`

The question asks for the probability

`P(3) or P(4) or P(5) or P(6)`

where "or" refers to the union of the probabilities of two or more possible outcomes.

Using conventional notation this is written as

`P(3) uu P(4) uu P(5) uu P(6)`

Unions are found by addition (compare with intersections, which are found by multiplication in conditional probability), so the required overall probability is

`1/6 + 1/6 + 1/6 + 1/6 = 4/6 = 2/3`